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Two-stage proportionate flexible flow shop to minimize the makespan

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Abstract

We consider a two-stage flexible flow shop problem with a single machine at one stage and m identical machines at the other stage, where the processing times of each job at both stages are identical. The objective is to minimize the makespan. We describe some optimality conditions and show that the problem is NP-hard when m is fixed. Finally, we present an approximation algorithm that has a worst-case performance ratio of \(\frac{5}{4}\) for m=2 and \(\frac{\sqrt{1+m^{2}}+1+m}{2m}\) for m≥3.

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Authors and Affiliations

  1. Department of Business Administration, Chungnam National University, 79 Daehangno, Yuseong-gu, Daejeon, 305-704, Korea

    Byung-Cheon Choi

  2. Department of Supply Chain Management & Marketing Sciences, Rutgers Business School, The State University of New Jersey, 1 Washington Park, Newark, NJ, 07102, USA

    Kangbok Lee

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  1. Byung-Cheon Choi
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  2. Kangbok Lee
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Correspondence to Kangbok Lee.

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Choi, BC., Lee, K. Two-stage proportionate flexible flow shop to minimize the makespan. J Comb Optim 25, 123–134 (2013). https://doi.org/10.1007/s10878-011-9423-1

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  • DOI: https://doi.org/10.1007/s10878-011-9423-1

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